Question

In a figure ray BA ll ray DE <c=50° and <d=100° ​

Answer 1

• Draw a line XY passing through point C and parallel to line AB as shown in figure,

⇔we have, AB ll DE and AB ll XY

♦ if two lines in a plane are parallel to a third line in the plane, then those two lines are parallel to each other.

• DE ll XY

ˢᴵᴺᶜᴱ ᴰᴱ ˡˡ ˣʸ ᴬᴺᴰ ᴰᶜ ᴵˢ ᵀᴿᴬᴺˢⱽᴱᴿˢᴬᴸ ᴵᴺᵀᴱᴿˢᴱᶜᵀᴵᴺᴳ ᵀᴴᴱᴹ ᴬᵀ ᴰ ᵃⁿᵈ c

then, ∠EDC + ∠YCD = 180°

( pairs of interior angles on the same side of transversal are supplementary )

⇒100⁰ + ∠YCD = 180⁰

⇒∠YCD = 180⁰ - 100⁰

∠YCD = 80⁰

• since, sum of all the angles on a straight line at a point is 180⁰ then,

⇒∠XCB + ∠BCD + ∠YCD = 180⁰

⇒∠XCB + 50⁰ + 80⁰ = 180⁰

⇒∠XCB + 130⁰ = 180⁰

⇒∠XCB = 180⁰ - 130⁰

⇒∠XCB = 50⁰

→ since, AB ll XY and BC is transversal intersecting them at B and C,

∠ABC + ∠XCB = 180⁰ ( ᵖᵃᶦʳˢ ᵒᶠ ᶦⁿᵗᵉʳᶦᵒʳ ᵃⁿᵍˡᵉˢ ᵒⁿ ᵗʰᵉ ˢᵃᵐᵉ ˢᶦᵈᵉ ᵒᶠ ᵗʳᵃⁿˢᵛᵉʳˢᵃˡ ᵃʳᵉ ˢᵘᵖᵖˡᵉᵐᵉⁿᵗᵃʳʸ)

⇒∠ABC + 50⁰ = 180⁰

→ ∠ABC = 130⁰